A modified Johnson-Cook (J-C) constitutive model considering pre-strain hardening for two-step electromagnetic forming

The classical Johnson-Cook (J-C) constitutive model is widely applied in the high strain rate-forming for sheet metal. If the classical J-C model is continuously adopted to analyze the dynamic deformation behavior of material in multi-step high strain rate forming, it may be difficult to have sufficient prediction accuracy. To address this limitation, this paper proposes a constitutive model, considering pre-strain hardening for the two-step electromagnetic forming (EMF) of 5A06 aluminum alloy (AA5A06) sheets, which introduces the polynomial functions of dynamic pre-strain to modify the initial yield stress, strength coefficient, and strain hardening exponent in the classical J-C model. The modified J-C model and the classical J-C model are incorporated into a unified constitutive model for two-step dynamic deformation. By means of quasi-static, fully dynamic, and two-step dynamic tensile tests, the mechanical property curves are obtained to determine the model parameters for AA5A06. Then, the modified constitutive model is programmed into finite element software via a user-defined subroutine, to predict the profiles of two-step EMF parts. The modified model theoretically captures the fact that, as the dynamic pre-strain increases, the yield stress of AA5A06 during second-step dynamic deformation increases in succession, while the strength coefficient and strain hardening exponent exhibits the variation trends of "U" and horizontal "S" shapes, respectively. Comparing the results from experiments and simulations shows that the prediction errors of the modified J-C model for all two-step EMF parts are within 6 %. The prediction accuracy of the modified model can be improved by up to 245 %, compared to the classical model, with the minimum prediction error for the final profile being only 1.5 %, compared to the experimental results. This demonstrates that the modified constitutive model is meaningful for guiding the application of multi-step EMF for sheet metal. To explain the differences in profiles of two-step EMF parts, the dynamic deformation behavior is reasonably explained by the strain distributions from simulation results.